Question

If rootx=7-3root2 find the value if rootx+1/rootx

Answer 1

Answer:

$210 - 90 \sqrt{2}$

Step-by-step explanation:

$\sqrt{x} = 7 - 3 \sqrt{2}$

$\frac{1}{ \sqrt{x} } = \frac{1}{7 - 3 \sqrt{2} }$

$\frac{1}{ \sqrt{x } } = \frac{7 + 3 \sqrt{2} }{(7 - 3 \sqrt{2})(7 + 3 \sqrt{2} ) }$

$\frac{1}{ \sqrt{x} } = \frac{7 + 3 \sqrt{2} }{49 - 18}$

$\frac{1}{ \sqrt{x} } = \frac{7 + 3 \sqrt{2} }{31}$

$\sqrt{x} + \frac{1}{ \sqrt{x} } = 7 - 3 \sqrt{2} + \frac{7 + 3 \sqrt{2} }{31}$

$\sqrt{x} + \frac{1}{ \sqrt{x} } = \frac{217 - 93 \sqrt{2} + 7 + 3 \sqrt{2} }{31}$

$\sqrt{x} + \frac{1}{ \sqrt{x} } = 210 - 90 \sqrt{2}$